Fitting GARCH models to stock data
The top graph in Figure 10.10 shows the percentage daily returns of the Dow Jones Industrial Index for the period July 1st, 1997, through April 9th, 1999, contained in the file E1032.TSM. The graph suggests that there are sustained periods of both high volatility (in October, 1997, and August, 1998) and of low volatility. The sample autoc orrelation function of this series has very small values, however the sample auto correlations of the absolute values and squares of the data are significantly different from zero, indicating dependence in spite of the lack of autocorrelation. (The sample auto correlations of the absolute values and squares of the residuals (or of the data if no transformations have been made and no model fitted) can be seen by clicking on the third green button at the top of the ITSM window.) These properties suggest that an ARCH or GARCH model might be appropriate for this series.